Modal and vectorial analysis for determination of stress axes associated with fault slip data

Abstract

Based on Anderson's faulting theory, for a given set of fault slip data including the sense of slip on faults and fault planes, this paper provides two possible methods to reconstruct the principal stress axes using vectorial and modal analysis procedure. The vectorial analysis consists of computing eigenvectors of the orientation matrices defined by axes Pϑ, B, and Tϑ (Pϑ, B, and Tϑ being geometrical axes parallel to axes σ1, σ2, σ3 associated with a single striated fault) which are determined geometrically knowing the slip vector S, the normal to fault plane N, and the dihedral angle 2ϑ. A parameter R, related to the maximum eigenvalue of the orientation matrix and the size of data sample, is shown to be a good test value for the homogeneity of the data. A process of refinement of this parameter enables “bad” data (representing faults generated under different tectonic events) to be ignored in the final computation of the principal stress axes; results are thus significantly improved and the vectorial analysis procedure enables the orientation of stress to be numerically determined. On defining probability density regions around each Pϑ, B, and Tϑ axes that incorporate the variation of fault geometry, the modal analysis is carried out in two density functions established by a convolution process to locate modes which represent optimal locations of the principal stress axes in spherical space. Splitting of heterogeneous data samples into homogeneous subsets is achieved by a dynamical cluster procedure which enables the principal stress axes associated with each subset to be determined separately.